Consider a learning algorithm, which involves an internal call to an optimization routine such as a generalized eigenvalue problem, a cone programming problem or even sorting. Integrating such a method as a layer(s) w...
详细信息
ISBN:
(纸本)9781577358664
Consider a learning algorithm, which involves an internal call to an optimization routine such as a generalized eigenvalue problem, a cone programming problem or even sorting. Integrating such a method as a layer(s) within a trainable deep neural network (DNN) in an efficient and numerically stable way is not straightforward - for instance, only recently, strategies have emerged for eigendecomposition and differentiable sorting. We propose an efficient and differentiable solver for general linear programming problems which can be used in a plug and play manner within DNNs as a layer. Our development is inspired by a fascinating but not widely used link between dynamics of slime mold (physarum) and optimization schemes such as steepest descent. We describe our development and show the use of our solver in a video segmentation task and meta-learning for few-shot learning. We review the existing results and provide a technical analysis describing its applicability for our use cases. Our solver performs comparably with a customized projected gradient descent method on the first task and outperforms the differentiable CVXPY-SCS solver on the second task. Experiments show that our solver converges quickly without the need for a feasible initial point. Our proposal is easy to implement and can easily serve as layers whenever a learning procedure needs a fast approximate solution to a LP, within a larger network.
Network bandwidth reservation is a representative service, where users directly reserve network resources on an ondemand basis. It utilizes the advantages of software defined networks, such as flexibility. To provide ...
详细信息
ISBN:
(纸本)9783903176362
Network bandwidth reservation is a representative service, where users directly reserve network resources on an ondemand basis. It utilizes the advantages of software defined networks, such as flexibility. To provide bandwidth reservation services extensively, an instantaneous response to user requests (e.g., less than 1 s) and a high user request acceptance ratio (e.g., over 90%) are required. In this study, we propose a bandwidth reservation method to meet these two requirements by combining machine learning (ML) and linear programming (LP), particularly for unpredictable bandwidth demands in which the usage time is strictly indicated. In the proposed method, a user request is instantaneously judged through ML, and network resource allocation, including traffic routing, is optimally determined through LP. We demonstrate that the proposed method provides a suboptimal acceptance ratio with a difference of less than 1% compared with the optimal solution and an instantaneous response of less than 0.1 ms under a general computation environment.
Community detection is a fundamental challenge in network science and graph theory that aims to reveal nodes' structures. While most methods consider Modularity as a community quality measure, Max-Min Modularity i...
详细信息
ISBN:
(纸本)9788395918384
Community detection is a fundamental challenge in network science and graph theory that aims to reveal nodes' structures. While most methods consider Modularity as a community quality measure, Max-Min Modularity improves the accuracy of the measure by penalizing the Modularity quantity when unrelated nodes are in the same community. In this paper, we propose a community detection approach based on linear programming using Max-Min Modularity. The experimental results show that our algorithm has a better performance than the previously known algorithms on some well-known instances.
This paper aims for reducing the energy demand in Morocco by means of developing the management system state-of-the-art. Three different scenarios are investigated, where dynamic pricing is applied along with effectiv...
详细信息
ISBN:
(纸本)9781665425483
This paper aims for reducing the energy demand in Morocco by means of developing the management system state-of-the-art. Three different scenarios are investigated, where dynamic pricing is applied along with effective appliance load scheduling to minimize the energy bill of the consumer. This paper starts by describing the current energy situation in Morocco with a focus on renewable energies. The paper defines a variety of dynamic pricing policies and describes the core model of home energy management systems. Three different scenarios are considered, each with different energy needs presented as sets of appliances classified in two distinct categories that serve as the main electricity load. The proposed model considers multiple constraints along with an optimization function that either minimizes the energy bill or maximizes the use of renewable energies generation within a household. MATLAB will be utilized to produce an adequate recommended schedule for each scenario. Results show that the proposed algorithms reduce the energy bill from 30% to 66% depending on the tested scenario, as a result of shifting up to 12 kWh of the load profile from the peak consumption hours to the hours where renewable energy generation is maximized.
In linear programming, many students find it difficult to translate a verbal description of a problem into a valid mathematical model. To better understand this, we examine the existing characteristics of college engi...
详细信息
In linear programming, many students find it difficult to translate a verbal description of a problem into a valid mathematical model. To better understand this, we examine the existing characteristics of college engineering students' errors across linear programming (LP) problems. We examined textbooks to identify the types of problems typically found in introductory linear programming courses. We then developed a comprehensive set of tasks and analyzed students' work to create a taxonomy of the errors and issues that students exhibited. From our findings, we define four categories of identified error types: (1) decision variable errors, (2) variable relationship errors, (3) notation errors, and (4) form errors. This study contributes to the research by investigating students' work in an area of undergraduate mathematics that has not been heavily explored before. Findings suggest specific areas of focus for future work in helping students develop their understanding of linear programming models and mathematical modeling in word problems in general.
The existence of strongly polynomial-time algorithm for linear programming is a cross century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artific...
详细信息
ISBN:
(纸本)9781450391153
The existence of strongly polynomial-time algorithm for linear programming is a cross century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artificial intelligence. In order to make it happen, this paper proposes three solving techniques based on the conecutting theory: 1. The selection of cutter: principles highest vs. deepest;2. The algorithm of column elimination, which is more convenient and effective than the Ye-column elimination theorem;3. A step-down algorithm for a feasible point horizontally shifts to the center and then falls down to the bottom of the dual feasible region D. There will be a nice work combining three techniques, the tri-skill is variant Simplex algorithm to be expected to help readers building the strong polynomial algorithms. Besides, a variable weight optimization method is proposed in the paper, which opens a new window to bring the linear programming into uncomplicated calculation.
The Polish economy is facing a huge challenge regarding the future of energy in Poland. The current energy system is very inefficient, it consumes huge resources that, like countries with high energy efficiency, could...
详细信息
The Polish economy is facing a huge challenge regarding the future of energy in Poland. The current energy system is very inefficient, it consumes huge resources that, like countries with high energy efficiency, could be allocated to the development of low-carbon and renewable energy networks. At the moment, the Polish energy sector, related to the coal monoculture, lacks electricity and the entire transmission system is obsolete. The solution may be distributed energy, which can ultimately satisfy energy supplies in less urbanized areas and in rural areas, while guaranteeing the sustainable development of these areas. In order to take up the challenge of better understanding and explaining such a complex reality, it was decided that the research framework of this article will be distributed energy in the region. The aim of the article is to ensure energy security in the conditions of innovative, ecological and open to competition regional energy using local energy resources. Currently, it is believed that distributed energy can be an effective solution to the problem of conventional energy operation.
This study seeks reflection on the approaches of 11th grade students to linear programming problems, discussing the approaches taken at different moments of the teaching process. It aims to analyze: How is the student...
详细信息
This study seeks reflection on the approaches of 11th grade students to linear programming problems, discussing the approaches taken at different moments of the teaching process. It aims to analyze: How is the students' mathematical competence characterized in relation to problemsolving;What differences can be identified in the resolutions at different moments of the teaching and learning process. We adopt a qualitative and interpretative methodology, analyzing the approaches of two pairs of students with different mathematical backgrounds. The analysis is guided by P ' olya's stages of solving a problem and aspects of the understanding of mathematical competence. The results show different approaches to the problems depending on the teaching moment and different competences. The mathematical background impacts the students' success when they implement routine procedures, however it does not seem to determine the students' competence to reason about a problem.
For the purpose of improving the capacity utilization rate of rail transit lines, combined with the expansion network of rail transit space-time passenger flow, a linear programming model for subway peak single-line p...
详细信息
ISBN:
(数字)9781728194097
ISBN:
(纸本)9781728194097
For the purpose of improving the capacity utilization rate of rail transit lines, combined with the expansion network of rail transit space-time passenger flow, a linear programming model for subway peak single-line passenger flow control with the goal of maximizing passenger turnover is established. The model can be directly solved using the Lpsolve solver. In the solution, the OD passenger flow and passenger flow control data of each train and each station can be obtained separately. Taking the morning peak passenger flow data of a certain line of Shenzhen Metro as an example, the passenger flow control method of each station in each period when the passenger flow of the whole line is maximized is solved. The calculation results show that the increase of the maximum number of waiting trains can increase the passenger turnover and passenger flow in the line, and can reduce the number of stations and the rate of flow control in the same period.
This paper describes the modelling of short-term generation capacity expansion planning (GCEP) for multi terminal VSC-based HVDC transmission systems. The GCEP formulation is based on a mixed-integer linear programmin...
详细信息
This paper describes the modelling of short-term generation capacity expansion planning (GCEP) for multi terminal VSC-based HVDC transmission systems. The GCEP formulation is based on a mixed-integer linear programming (MILP) framework where transmission losses are considered by piecewise linearisation. As opposed to existing methods, the present GCEP formulation is based on shift factors which enable the representation of the hybrid AC/DC grids including VSC stations. This way new power generation investments can be efficiently determined at any of the VSC-connected AC systems. This new method lies in sharp contrast with the so-called classic GCEP method where the system nodal power balances are formulated using the voltage phase angles as decision variables thus increasing the model complexity. Indeed, to determine the GCEP investments, the present model aimed to multi-terminal HVDC links only uses AC/DC transmission line losses, power generations and projected generating power plants as decision variables. The new GCEP formulation is compared to the classic method using two compelling multi-terminal VSC-HVDC test systems for validity and applicability purposes. Results show that the proposed formulation reduces the simulation running time by more than 80%, compared to the standard model, accompanied by acceptable accuracy of results since errors inferior to 5% are obtained.
暂无评论